Finite Group DatabasebetaFinite Group Databasebeta| order | 720 |
| isoclinism | isoclinic class of D5 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C9 · Schur multiplier (H2) = C23 |
| direct product | C2×C4×C9×D5 |
| Fitting | C2×C4×C5×C9 ⋊ C2 |
| derived, Sylow | C5 ⋊ C22×C4×C9 |
| Hall | C5×C9 ⋊ C22×C4 |
162 conjugacy classes of subgroups.
| transitive degree | μt(G) = 360 |
288 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #13083744, C9×#3952, C9×#4003, … |
| maximal normal subgroup of | #13083744, C9×#3952, C9×#4003, … |
| maximal quotient of | C4×C9×Dic10, C42×C9×D5, C9×#4018, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(720, 156);